Ab initio calculation of electronic structure

A crucial feature of PNC experiments in atoms, molecules, liquids or solids is that for interpretation of measured data in terms of fundamental constants of the P,T-odd interactions, one must calculate those properties of the systems, which establish a connection between the measured data and studied fundamental constants (see section 4). These properties are described by operators heavily concentrated near or on heavy nuclei they cannot be measured and their theoretical study is not a trivial task. During the last several years the significance of (and requirement for) ab initio calculation of electronic structure providing a high level of reliability and accuracy in accounting for both relativistic and correlation effects has only increased (see sections 3 and 10). 

Since the early days of quantum mechanics, the wave function theory has proven to be very successful in describing many different quantum processes and phenomena. However, in many problems of quantum chemistry and solid-state physics, where the dimensionality of the systems studied is relatively high, ab initio calculations of the structure of atoms, molecules, clusters, and crystals, and their interactions are very often prohibitive. Hence, alternative formulations based on the direct use of the probability density, gathered under what is generally known as the density matrix theory [1], were also developed since the very beginning of the new mechanics. The independent electron approximation or Thomas-Fermi model, and the Hartree and Hartree-Fock approaches are former statistical models developed in that direction [2]. These models can be considered direct predecessors of the more recent density functional theory (DFT) [3], whose principles were established by Hohenberg,... 

Hartree-Fock theory is a rigorous ab initio theory of electronic structure and has a vast array of successes to its credit. Equilibrium structures of most molecules are calculated almost to experimental accuracy, and reasonably accurate properties (e.g., dipole moments and IR and Raman intensities) can be calculated from HF wave functions. Rela-... 

G.-M. Rignanese, X. Gonze, A. Pasquarello, "Ab-Initio Calculations of the Structural, Electronic and Dynamical Properties of High-k Dielectrics", Ed. M. Houssa, Institute of Physics Publishing, 2004, pp 431. 

Two of the hydrophihcity scales in Table 2 were derived from experimental measures of the behavior of amino acids in various solvents, namely partitioning coefficients [K-D index of Kyte and Doolittle (30)] or mobility in paper chromatography [Rf index of Zimmerman et al. (31)]. By contrast, the Hp index was obtained from quantum mechanics (QM) calculations of electron densities of side chain atoms in comparison with water (32). The Hp index is correlated highly with these two established hydrophobicity scales (Table 4). Therefore, like the polarizability index, it is possible to represent fundamental chemical properties of amino acids (hydrophUicity, Hp) with parameters derived from ab initio calculations of electronic properties. However, in contrast to polarizabihty (steric effects), hydrophihcity shows significant correlation with preference for secondary structure. Thus, hydrophobic amino acids prefer fi-strands (and fi-sheet conformations) and typically are buried in protein structures, whereas hydrophilic residues are found commonly in turns (coil structure) at the protein surface. 

We have performed ab initio calculations of electronic band structures of nonhydrogenated silicon nanowires in the <001>, <011>. <111> and <112> orientations. Our results clearly indicate that silicon nanowires with the <001>, <111> and <112> axes have turned out to be metallic, while the one with the <011> axis displays the semiconducting behavior. 

ESC electronic structure calculation ab initio calculation of electron densities)... 

Jurgen Fritsch and Pasquale Pavone, Ab initio calculation of the structure, electronic states, and the phonon dispersion of the Si(lOO) surface, Surface Science, V344,159(1995). 

FIGURE 2. (a) Coordinate system of [Au(8a)2] used in the ab initio calculation (b) electronic structure in the valence region of I = [Au(8a)2] (left) and la = [Au(8a)2] (right). Reprinted with permission from Reference 20. Copyright (1995) American Chemical Society... 

Wang, X. Q., Clark, S. J., 8c Abram, R. A. (2004). Ab initio calculations of the structural and electronic properties of HgmTe cluster. Physical Review B - Condensed Matter and Materials Physics, 70(23), 1-6. 

Not all iterative semi-empirical or ab initio calculations converge for all cases. For SCF calculations of electronic structure, systems with a small energy gap between the highest occupied orbital and the lowest unoccupied orbital may not converge or may converge slowly. (They are generally poorly described by the Hartree-Fock method.)... 

The ab initio calculations of various three-electron hemibonded systems [122, 123] indicated that the inclusion of electron correlation corrections is extremely important for the calculation of three-electron bond energies. The Hartree-Fock (HF) error is found to be nonsystematic and always large, sometimes of the same order of magnitude as the bond energy. According to valence bond (VB) and MO theories, the three-electron bond is attributed to a resonance between the two Lewis structures... 

Doms, L., H. J. Geise, C. Van Alsenoy, L. Van den Enden, and L. Schafer. 1985. The Molecular Orbital Constrained Electron Diffraction (MOCED) Structural Model of Quadricyclane Determined by Electron Diffraction Combined with Ab Initio Calculations of Potential and Geometrical Parameters. J. Mol. Struct. 129, 299-314. 

For earlier ab initio calculations of the electronic structure of 1,3-butadiene see Refs.195 and 196). 

In excerpt 3Y, the authors refer to computational results performed with the Gaussian suite of programs, a computational package used to calculate molecular ab initio or semiempirical electronic structure theory. Computational parameters (e.g., the basis set and level of theory) are included in the description. Do not worry if you do not understand the content of excerpt 3Y the language is intended for chemists with a computational or theoretical background. 

The electronic structure parameters describing the P,T-odd interactions of electrons (sections 7, 8, and 10) and nucleons (section 9) including the interactions with their EDMs should be reliably calculated for interpretation of the experimental data. Moreover, ab initio calculations of some molecular properties are usually required even for the stage of preparation of the experimental setup. Thus, electronic structure calculations suppose a high level of accounting for both correlations and relativistic effects (see below). Modern methods of relativistic ab initio calculations (including very... 

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